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Find $ f'(x). $ Check that your answer is reasonable by comparing the graphs of $ f $ and $ f'. $$ f(x) = \sqrt {1 - x^2} \arcsin x $

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$\frac{-x \arcsin x + 1}{\sqrt{1-x^{2}}}$

00:42

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 5

Implicit Differentiation

Derivatives

Differentiation

Nathan C.

October 27, 2021

good video but maybe go a bit slower

Oregon State University

Baylor University

University of Michigan - Ann Arbor

Boston College

Lectures

04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

44:57

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

01:25

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in this problem, we're given a function of X. And whereas Thio find narrative from Ex Lester out, that's like there with old suspect X. We're gonna support a cruel so the first time they talk that it's one over to skirt off, all minus expert but supplied by the village of in a function or the parents of infection Later, two X terms are excited bags, plus skirted of one minus. X squared is first year, most part by their second. We're goingto port side effects is one of our spirit for months. Expert. So these will cancel out, and we will find a way to permit tax as, um, off your shoes can slap negative X divided by skirted off one one's expert times Art Sina Bucks plus one. The few graft, Equifax and private fax where this record is perfect and it's blue ones that prime effects you could use another function porter. We see that it makes sense because whenever function goes from decreasing to increasing the they're interchanges sign and it goes from negative 2002. Also same behavior. Whatever function starts decreasing right At this point, it was increasing here only 23 At this point, there was a genius sign, and this time it goes from positive to negative

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